If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
A. 20
B. 40
C. 50
D. 80
E. 120
Answer: D
Source: Official Guide
If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two
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Take the task of creating a committee and break it into stages.Gmat_mission wrote: ↑Thu Jul 22, 2021 10:47 amIf a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
A. 20
B. 40
C. 50
D. 80
E. 120
Answer: D
Source: Official Guide
Stage 1: Select 3 COUPLES
Since the order in which we select the couples does not matter, we can use COMBINATIONS
We can select 3 couples from 5 couples in 5C3 ways ( = 10 ways)
ASIDE: If anyone is interested, we have a video on calculating combinations (like 5C3) in your head (see bottom of post)
At this point, we have selected 3 COUPLES, which we'll call A, B and C. We're now going to select ONE person from each couple to be on the committee.
Stage 2: Select 1 person from couple A
There are 2 people in this couple, so we can complete this stage in 2 ways.
Stage 3: Select 1 person from couple B
There are 2 people in this couple, so we can complete this stage in 2 ways.
Stage 4: Select 1 person from couple C
There are 2 people in this couple, so we can complete this stage in 2 ways.
By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create a 3-person committee) in (10)(2)(2)(2) ways (= 80ways)
Answer: D